Correction method and equipment for ellipsometry and storage medium

Abstract

The invention discloses a correction method and device for ellipsometry, and a storage medium. The method comprises the following steps: collecting energy intensity distribution of a light spot at an exit pupil plane position of an incident arm lens; on the basis of energy intensity distribution, a discretized intensity distribution dot matrix is generated in a self-adaptive mode, and the normalized weight of each point is calculated; establishing a discretized numerical aperture distribution function based on the intensity distribution dot matrix, the normalized weight and the lens numerical aperture parameter; and correcting a depolarization effect in spectral ellipsometry by using the numerical aperture distribution function to obtain a measurement result of the optical critical dimension or the film thickness. According to the method, the accurate numerical aperture model is established through the real light spot characteristics, the problem of measurement errors caused by light spot deformation caused by the diaphragm is effectively solved, the accuracy and reliability of optical critical dimension or film thickness measurement are remarkably improved, and meanwhile the method has the advantages of being low in implementation cost and high in adaptability.

Description

Technical Field

[0001] This application relates to the fields of semiconductor manufacturing and precision optical measurement technology, and in particular to a correction method, apparatus and storage medium for ellipsometric measurement. Background Technology

[0002] In the fields of semiconductor manufacturing and precision optical component production, high-precision measurement of micro- and nanostructures such as thin film thickness and critical dimensions is crucial. Optical critical dimension or film thickness measurement technology, as a core component in these fields, directly impacts product performance and yield. Spectral ellipsometric measurement technology is widely used due to its non-contact and high-precision characteristics. Numerical aperture, a common depolarization source introduced by the device in optical systems, plays a decisive role in obtaining high-quality measurement results through accurate setting and model correction. In conventional ellipsometric measurement system architectures, the introduction of an aperture is a common means of achieving optical path control and optimizing measurement conditions. However, by limiting the propagation range of the light beam, the aperture inevitably alters the original ideal circular shape of the light spot, causing the actual light spot to exhibit complex rectangular, elliptical, or other irregular shapes.

[0003] Currently, the commonly used method is to derive a hypothetical numerical aperture distribution function based on experience or a simple lens model, usually derived from an ideal circular light spot. However, when the light spot is deformed due to the aperture stop, the numerical aperture calculation formula derived from a circular light spot can no longer accurately reflect the actual transmission path and energy distribution characteristics of light within the optical system. This mismatch means that continuing to use traditional numerical aperture data for system analysis and measurement result correction fails to accurately reflect the actual working state of the measurement system, and corresponding corrections are unlikely to effectively improve measurement results, ultimately limiting the accuracy of critical optical dimensions or film thickness measurements. Summary of the Invention

[0004] In view of this, this application provides a correction method, device and storage medium for ellipticity measurement to solve the problem of insufficient measurement accuracy caused by the mismatch between the numerical aperture model and the actual light spot in the prior art.

[0005] To solve the above-mentioned technical problems, one technical solution adopted in this application is: to provide a correction method for ellipticity measurement, comprising: The energy intensity distribution of the light spot is collected at the exit pupil surface of the incident arm lens; Based on the energy intensity distribution, a discretized intensity distribution lattice is adaptively generated, and the normalized weight of each point is calculated. Based on the intensity distribution lattice, normalized weights, and lens numerical aperture parameters, a discretized numerical aperture distribution function is established. The depolarization effect in spectral ellipsometric measurement is corrected by using the numerical aperture distribution function to obtain the measurement results of optical critical dimensions or film thickness.

[0006] As a further improvement to this application, based on the energy intensity distribution, a discretized intensity distribution lattice is adaptively generated, and the normalized weight of each point is calculated, including: Based on the energy intensity distribution, an adaptive threshold method is used to identify the effective area of ​​the light spot; Based on the shape parameters and / or spot energy distribution of the effective area, match the lattice configuration; Based on the lattice configuration and energy intensity distribution, the normalized weight of each point is calculated.

[0007] As a further improvement to this application, an adaptive thresholding method is used to identify the effective region of the light spot, including: Select the pixel region whose energy intensity is greater than the maximum intensity by a preset percentage as the effective region.

[0008] As a further improvement to this application, based on the shape parameters of the effective region, the matching dot matrix configuration includes: Calculate the rectangularity or roundness of the effective region; When the rectangularity is higher than the first threshold, the shape of the light spot is determined to be rectangular, and a dot matrix configuration that is suitable for the rectangular light spot is matched. When the roundness is higher than the second threshold, the shape of the light spot is determined to be elliptical or circular, and a dot matrix configuration that is suitable for the elliptical or circular light spot is matched.

[0009] As a further improvement to this application, based on the spot energy distribution of the effective region, a matching dot matrix configuration is made, including: Spatial distribution features of the light spot energy distribution in the effective area are extracted, and the energy gradient is calculated to identify whether there are step features formed by energy jumps in the energy distribution; If an energy step is detected, edge detection is performed on the energy distribution of the light spot. The detected edges of each step are used as spatial boundaries, and the effective area is divided into discrete regions with an appropriate dot matrix configuration. If no obvious energy step is identified, multiple equal-energy-level envelopes are preset based on the peak ratio or curvature change rate of the energy distribution to virtually divide the effective area and obtain multiple regions that are adapted to the lattice configuration.

[0010] As a further improvement to this application, the normalized weights for each point are calculated, including: Map the matched dot matrix configuration to the valid area, treating each dot as an integral unit; The sum of the energy intensities of all pixels within each integration unit is calculated to obtain the integrated light intensity of each unit; Sum all the integrated light intensities to obtain the total light intensity; Divide the integrated light intensity of each unit by the total light intensity to obtain the normalized weight corresponding to that point.

[0011] As a further improvement to this application, a discretized numerical aperture distribution function is established, including: Based on the normalized coordinates of each sampling point on the exit pupil plane and the lens numerical aperture parameters, the incident angle and azimuth angle corresponding to each sampling point are calculated through geometric optical relationships, forming a set of triplet sequences consisting of incident angle, azimuth angle and normalized weights, which serve as the discretized numerical aperture distribution function.

[0012] As a further improvement to this application, the depolarization effect in spectral ellipsometric measurement is corrected using a numerical aperture distribution function to obtain measurement results for optical critical dimensions or film thickness, including: The ellipsometry of the target sample was obtained by testing, and the Mueller matrix spectrum of the first sample was obtained. Spectrum of the average Mueller matrix of the first model was calculated based on the numerical aperture distribution function; By fitting the Mueller matrix spectrum of the first sample with the average Mueller matrix spectrum of the first model, the optical critical dimensions or film thickness can be obtained.

[0013] As a further improvement to this application, before correcting the depolarization effect in spectral ellipsometric measurements using the numerical aperture distribution function, the following is also included: Ellipsometry was performed using a standard sample with a known film thickness to obtain the Mueller matrix spectrum of the second sample; Spectrum of the average Mueller matrix of the second model was calculated based on the numerical aperture distribution function; The fitted film thickness value is obtained by fitting the Mueller matrix spectrum of the second sample with the average Mueller matrix spectrum of the second model. The numerical aperture parameters of the lens are fine-tuned based on the fitted film thickness to optimize the numerical aperture distribution function.

[0014] As a further improvement to this application, a nonlinear regression algorithm or library matching algorithm is used to fit the Mueller matrix spectrum of the first sample to the average Mueller matrix spectrum of the first model and / or a nonlinear regression algorithm or library matching algorithm is used to fit the Mueller matrix spectrum of the second sample to the average Mueller matrix spectrum of the second model.

[0015] To solve the above-mentioned technical problems, another technical solution adopted in this application is: to provide a correction device for ellipticity measurement, which includes: The acquisition module is used to acquire the energy intensity distribution of the light spot at the exit pupil surface of the incident arm lens; The generation module is used to adaptively generate a discretized intensity distribution lattice based on the energy intensity distribution and calculate the normalized weight of each point; A module is established to create a discretized numerical aperture distribution function based on the intensity distribution lattice, normalized weights, and lens numerical aperture parameters. The correction module is used to correct the depolarization effect in spectral ellipsometric measurement using the numerical aperture distribution function, so as to obtain the measurement results of optical critical dimensions or film thickness.

[0016] To solve the above-mentioned technical problems, another technical solution adopted in this application is: to provide a computer device, the computer device including a processor and a memory coupled to the processor, the memory storing program instructions, and when the program instructions are executed by the processor, causing the processor to perform the steps of the elliptic measurement correction method as described above.

[0017] To solve the above-mentioned technical problems, another technical solution adopted in this application is to provide a storage medium storing program instructions capable of implementing the correction method for ellipsometric measurement as described above.

[0018] The beneficial effects of this application are: The ellipsometric correction method, device, and storage medium of this application directly acquire and analyze the energy intensity distribution of real light spots, adaptively generate discretized lattices and normalized weights, and establish a numerical aperture distribution function that accurately matches the actual optical path state. This significantly improves the measurement accuracy and reliability of key optical dimensions or film thickness. Through weight calculation based on real light intensity and adaptive lattice distribution, the numerical aperture model closely matches the actual optical system. It has strong adaptability and can intelligently cope with various regular and irregular light spot shapes generated by different device optical paths. While ensuring accuracy, it optimizes the utilization of computational resources and achieves a balance between measurement efficiency and accuracy. This method does not require hardware modification and can be implemented only through algorithm upgrades. It is low-cost and easy to integrate into existing ellipsometric measurement equipment, and has extremely high application value in the fields of semiconductor manufacturing and precision optical measurement. Attached Figure Description

[0019] Figure 1 This is a schematic flowchart of a correction method for ellipticity measurement according to an embodiment of the present invention; Figure 2 This is a schematic diagram of a 3×3 dot matrix distribution according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the (2,3,2) dot matrix distribution according to an embodiment of the present invention; Figure 4 This is a schematic diagram of a 9×1 dot matrix distribution according to an embodiment of the present invention; Figure 5 This is a schematic diagram of the functional modules of the correction device for ellipticity measurement according to an embodiment of the present invention; Figure 6 This is a schematic diagram of the structure of a computer device according to an embodiment of the present invention; Figure 7 This is a schematic diagram of the structure of the storage medium according to an embodiment of the present invention. Detailed Implementation

[0020] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0021] The terms "first," "second," and "third" in this application are for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first," "second," or "third" may explicitly or implicitly include at least one of that feature. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified. All directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of this application are only used to explain the relative positional relationships and movements between components in a specific orientation (as shown in the figures). If the specific orientation changes, the directional indications also change accordingly. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or devices.

[0022] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0023] Figure 1 This is a schematic flowchart of the correction method for ellipticity measurement according to an embodiment of the present invention. It should be noted that if substantially the same result is obtained, the method of the present invention is not necessarily identical. Figure 1 The illustrated process sequence is limited. For example... Figure 1 As shown, the correction method for ellipticity measurement includes the following steps: Step S1: Collect the energy intensity distribution of the light spot at the exit pupil surface of the incident arm lens.

[0024] Specifically, in practice, a high-resolution CCD device is placed at the exit pupil of the incident lens to directly capture the original energy intensity distribution of the light spot. During implementation, the CCD device's resolution should be high enough to ensure accurate capture of the light spot's detailed features. The acquired energy intensity distribution is a two-dimensional matrix, where the value of each pixel represents the light intensity at that location. This data accurately reflects the actual shape of the light spot after aperture cropping, which may be rectangular, elliptical, or other irregular shapes.

[0025] Step S2: Based on the energy intensity distribution, adaptively generate a discretized intensity distribution lattice and calculate the normalized weight of each point.

[0026] Specifically, this embodiment designs an adaptive intelligent algorithm to transform the energy intensity distribution of the light spot into a discrete mathematical model composed of a finite number of sampling points and their corresponding weights. It abandons the traditional mode of preset fixed dot matrix and instead automatically completes effective region identification, shape discrimination, dot matrix configuration and weight calculation based on the natural shape and energy distribution of the real light spot, thereby laying a precise data foundation for the subsequent construction of a high-fidelity numerical aperture distribution function.

[0027] Furthermore, step S2 specifically includes: 1. Based on the energy intensity distribution, the effective area of ​​the light spot is identified using an adaptive threshold method.

[0028] The step of identifying the effective area of ​​the light spot using the adaptive threshold method specifically includes: selecting a pixel area with an energy intensity greater than the maximum intensity by a preset percentage as the effective area.

[0029] Specifically, an adaptive thresholding method is used to process the original light spot image. Specifically, the maximum light intensity value in the image is first located. Then set a threshold (e.g.) All pixels with light intensity below this threshold are considered background noise and excluded. The remaining pixel area is defined as the effective area of ​​the light spot. This effectively removes background noise interference, ensuring that all subsequent processing is based on the area that actually carries light energy. This guarantees the purity and reliability of the input data, eliminates stray light and noise interference, and ensures that subsequent processing is only applied to the area of ​​the light spot that truly carries energy. The preset percentage is preferably set to 1%, which can be adjusted according to the actual measurement environment and accuracy requirements. In high-precision measurement environments, it can be set to 0.5% or lower.

[0030] 2. Match the dot matrix configuration based on the shape parameters and / or spot energy distribution of the effective area.

[0031] Specifically, this embodiment configures the dot matrix by analyzing the shape parameters and / or energy distribution of the effective area.

[0032] Furthermore, the step of matching the dot matrix configuration based on the shape parameters of the effective region specifically includes: 2.01. Calculate the rectangularity or roundness of the effective area.

[0033] 2.02. When the rectangularity is higher than the first threshold, the shape of the light spot is determined to be rectangular, and a dot matrix configuration adapted to the rectangular light spot is matched.

[0034] 2.03. When the roundness is higher than the second threshold, the shape of the light spot is determined to be elliptical or circular, and a dot matrix configuration adapted to the elliptical or circular light spot is matched.

[0035] Specifically, the formula for calculating rectangularity is: Rectangularity = Effective area area / Minimum bounding rectangle area. When rectangularity is close to 1, it indicates that the spot shape is close to a rectangle. The formula for calculating roundness is: Roundness = 4π × Effective area area / Perimeter². When roundness is close to 1, it indicates that the spot shape is close to a circle or ellipse. The first and second thresholds are preset. When rectangularity is higher than the first threshold (e.g., 0.85), the spot shape is determined to be rectangular, and a 3×3 match is performed (e.g., ...). Figure 2 (As shown) or a dot matrix configuration of shapes such as 4×2; when the roundness is higher than the second threshold (e.g., 0.8), the shape of the light spot is determined to be elliptical, and can be matched as (2,3,2) (e.g. Figure 3 The dot matrix configuration is shown in the figure. Furthermore, the choice of dot matrix configuration must consider the balance between computational resources and accuracy requirements. A 3×1 dot matrix is ​​suitable for situations with limited computational resources; 3×3, 4×2, etc., dot matrices are suitable for clearly rectangular spots; and (2,3,2) dot matrices are suitable for elliptical spots. In addition, for elongated spots, rectangularity or roundness can be disregarded, and the dot matrix can be divided into an N×1 dot matrix, for example, a 9×1 dot matrix (as shown in the figure). Figure 4 (As shown) dot matrix.

[0036] Furthermore, based on the spot energy distribution in the effective area, the matching dot matrix configuration includes: 2.11. Extract the spatial distribution features of the light spot energy distribution in the effective area, and identify whether there are step features formed by energy jumps in the energy distribution by calculating its energy gradient; 2.12. If an energy step is detected, edge detection is performed on the energy distribution of the light spot. The detected edges of each step are used as spatial boundaries, and the effective area is divided into discrete areas with an appropriate dot matrix configuration. 2.13. If no obvious energy step is identified, multiple iso-energy level envelopes are preset based on the peak ratio or curvature change rate of the energy distribution to virtually divide the effective area and obtain multiple areas that are adapted to the lattice configuration.

[0037] Specifically, when configuring the dot matrix, the spatial distribution features of the acquired spot energy distribution are first extracted, and the presence of energy step features is identified by calculating the energy gradient. If energy steps exist, edge detection is performed on the spot energy distribution, and the edges of each step are used as spatial boundaries to divide the spot into discrete regions that fit the preset dot matrix. If the energy distribution is smooth and there are no obvious steps, an equal-level envelope is preset based on the energy peak ratio or curvature change rate to achieve virtual division of the spot region. This enables effective and high-fidelity sampling of the spot energy distribution features under sparse dot matrix conditions.

[0038] 3. Calculate the normalized weight of each point based on the lattice configuration and energy intensity distribution.

[0039] The steps for calculating the normalized weights of each point specifically include: 3.1 Map the matched dot matrix configuration to the effective area, treating each dot as an integral unit.

[0040] Specifically, firstly, a two-dimensional pixel coordinate system is established based on the energy intensity distribution image. For example, the top left corner of the image is the origin (0,0), and the bottom right corner is (width-1, height-1). Each "point" in the matched dot matrix configuration (e.g., 3×3) is understood as a position in normalized coordinates. For example, for a 3×3 dot matrix, the normalized coordinates of its center point might be (0.5, 0.5), and the coordinates of the bottom left corner point might be (0.1, 0.1). Then, based on the actual boundary of the effective spot area determined by the normalized coordinates, it is linearly mapped back to the specific pixel coordinates. At this point, each "point" is no longer an infinitesimal geometric point, but represents a region (i.e., an "integration unit"). This region is usually defined as a region centered on that point, divided by the boundaries of adjacent points. For internal points, the integration unit can be defined as a polygon enclosed by the perpendicular bisectors of the lines connecting adjacent points (i.e., the Voronoi diagram principle); for points on the boundary, the integration unit is determined by both the boundary of the effective region and the internal boundary. In practical programming, it is common practice to divide the effective area into several rectangular or square grids using a dot matrix configuration, with each grid serving as an integration unit. For example, a 3×3 dot matrix would divide the effective rectangular area into 9 smaller rectangles.

[0041] 3.2 Calculate the sum of the energy intensities of all pixels in each integration unit to obtain the integrated light intensity of each unit.

[0042] Specifically, for each defined integration unit, all pixels falling within that unit are iterated over, and the grayscale value (representing the energy intensity of that point) of each pixel within that integration unit is accumulated. For the i-th integration unit, its integrated light intensity... ,in It is the intensity value of pixel p. This represents the i-th integration unit. The final output is an integrated light intensity sequence equal to the number of points in the matrix. .

[0043] 3.3 Summing up all the integrated light intensities yields the total light intensity.

[0044] Specifically, total light intensity , This indicates the number of integration units.

[0045] 3.4 Divide the integrated light intensity of each unit by the total light intensity to obtain the normalized weight corresponding to that point.

[0046] Specifically, for the i-th point in the dot matrix, the light intensity of its corresponding integration unit is... Divide by total light intensity , is represented as: . The normalized weight of the i-th point represents the percentage contribution of the ray within the integration unit represented by the i-th sampling point to the entire ellipsometric measurement signal. For example, a point with a weight of 0.15 represents a ray that accounts for 15% of the contribution in the theoretical model.

[0047] Step S3: Based on the intensity distribution lattice, normalized weights, and lens numerical aperture parameters, establish a discretized numerical aperture distribution function.

[0048] Specifically, this embodiment uses intensity distribution lattice, normalized weights and lens numerical aperture parameters to generate a mathematical model that can accurately describe the actual working state of the optical system. The model, in the form of discrete data points, clarifies the incident angle of each representative ray and its weight in the final measurement result.

[0049] Furthermore, in step S3, the step of establishing the discretized numerical aperture distribution function specifically includes: calculating the incident angle and azimuth angle corresponding to each sampling point based on the normalized coordinates of each sampling point on the exit pupil plane and the lens numerical aperture parameters through geometric optical relationships, forming a set of triplet sequences composed of incident angle, azimuth angle and normalized weights, which serve as the discretized numerical aperture distribution function.

[0050] Specifically, firstly, a two-dimensional normalized coordinate system is established based on the exit pupil surface of the incident arm lens. Typically, the center of the exit pupil surface is set as the origin (0,0), and the edges are defined as the range from (-1,-1) to (1,1). This represents the horizontal coordinate of a point in the dot matrix. Represents the vertical coordinate.

[0051] According to geometric optics, at a certain point on the exit pupil plane... The angle at which the corresponding ray strikes the sample can be calculated as follows: 1. Calculate the angle of incidence. The angle of incidence of the light ray at this point. The position of the point on the exit pupil plane and the focal length of the lens ( Determined. The calculation formula is: This formula shows that the further a point is vertically from the center of the pupil (…). The larger the angle of incidence, the greater the angle of incidence. The larger it is.

[0052] 2. Calculate the azimuth angle : The azimuth angle corresponding to this point It refers to the orientation of the light ray within the plane of incidence, which can be calculated from its coordinates: , It is a four-quadrant arctangent function that can provide the correct angle value within the range of 0° to 360°.

[0053] After obtaining the incident angle, azimuth angle, and normalized weights, these three parameters are combined into a triple: The entire dot matrix (containing n dots) forms a sequence of n triples: .

[0054] Step S4: Use the numerical aperture distribution function to correct the depolarization effect in the spectral ellipsometric measurement to obtain the measurement results of the optical critical dimension or film thickness.

[0055] Specifically, this embodiment uses a numerical aperture distribution function to "simulate" the depolarization behavior of the optical system in theoretical calculations, thereby enabling the theoretical model to closely match the measured data. Ultimately, accurate sample parameters are derived through fitting. These key optical dimensions specifically include parameters such as critical dimensions, sidewall angles, height, and linewidth.

[0056] Furthermore, step S4 specifically includes: 1. The ellipsometry of the target sample was obtained by testing, and the Mueller matrix spectrum of the first sample was obtained.

[0057] Specifically, the target sample to be tested is placed on an ellipsometer and a standard spectral ellipsometric measurement is performed. The detector collects the polarized light signal after it passes through the sample. After data processing, the first sample Mueller matrix spectrum at different wavelengths is obtained.

[0058] 2. Calculate the average Mueller matrix spectrum of the first model based on the numerical aperture distribution function.

[0059] Specifically, using the numerical aperture distribution function The first model of computational theory, the average Mueller matrix spectrum. For each wavelength point, perform the following weighted average calculation: ,in, At a specific wavelength Angle of incidence Azimuth Under the given conditions, the Mueller matrix spectrum of the first sample is calculated based on an assumed sample model (such as a thin film stack model, a grating model, etc.). These are the corresponding weights in the numerical aperture distribution function.

[0060] 3. Fit the Mueller matrix spectrum of the first sample with the average Mueller matrix spectrum of the first model to obtain the optical key dimensions or film thickness.

[0061] Specifically, by continuously adjusting the parameters to be determined in the sample model (such as film thickness, linewidth, sidewall angle, etc.), the difference between the Mueller matrix spectrum of the first sample and the average Mueller matrix spectrum of the first model is minimized across the entire spectral range. When the fit reaches its optimum, the parameter values ​​in the sample model are the final measured optical critical dimensions or film thickness.

[0062] Furthermore, prior to step S4, the following steps are also included: 1.1. Ellipsometry was measured using a standard sample with a known film thickness to obtain the Mueller matrix spectrum of the second sample.

[0063] Specifically, a standard sample with a known film thickness (or critical dimension) and metrological verification is placed at the measurement position of the ellipsometer. Spectral ellipsometric measurements are performed using the exact same equipment configuration (including wavelength range, aperture size, etc.) as the target sample. The Mueller matrix spectra of the standard sample at different wavelengths are then obtained.

[0064] 1.2 Calculate the average Mueller matrix spectrum of the second model based on the numerical aperture distribution function.

[0065] Specifically, using the initial numerical aperture distribution function and based on the known structural parameters of the standard sample (such as the known film thickness), a theoretical model is established, and the corresponding second model average Mueller matrix spectrum is calculated.

[0066] 1.3. Fit the Mueller matrix spectrum of the second sample with the average Mueller matrix spectrum of the second model to obtain the fitted film thickness value.

[0067] 1.4. Fine-tune the numerical aperture parameters of the lens based on the fitted film thickness to optimize the numerical aperture distribution function.

[0068] Specifically, the nominal numerical aperture parameter of the lens As initial values, a nonlinear regression algorithm (such as the Levenberg-Marquardt algorithm) is used to match and fit the Mueller matrix spectrum of the second sample with the average Mueller matrix spectrum of the second model. During this fitting process, the film thickness of the standard sample is a fixed, known quantity, while the optimized parameter being fine-tuned is the numerical aperture value of the lens, making the fitted film thickness value close to the film thickness of the standard sample. The iteration stops when the difference between the Mueller matrix spectrum of the second sample and the average Mueller matrix spectrum of the second model reaches its minimum. The corresponding lens numerical aperture parameter at this point is the optimized lens numerical aperture parameter, which is then used to construct the numerical aperture distribution function. This embodiment maximizes the potential for depolarization correction by achieving optimal matching between the numerical aperture model and the real optical system, providing the highest achievable accuracy foundation for measuring target samples.

[0069] Furthermore, based on the above embodiments, in other embodiments, a nonlinear regression algorithm or library matching algorithm is used to fit the Mueller matrix spectrum of the first sample with the average Mueller matrix spectrum of the first model and / or a nonlinear regression algorithm or library matching algorithm is used to fit the Mueller matrix spectrum of the second sample with the average Mueller matrix spectrum of the second model.

[0070] The nonlinear regression algorithm aims to find a set of model parameters through iterative optimization that minimizes the difference (usually represented by the sum of squared residuals) between the spectral data output by the theoretical model and the spectral data obtained from experimental measurements. In this embodiment, the model parameters are the optical critical dimensions or film thicknesses to be determined, and the spectrum output by the theoretical model is the model-averaged Mueller matrix spectrum or the model-averaged Mueller matrix spectrum. Considering that spectral ellipsometry models are usually complex and have local optima, the Levenberg-Marquardt (LM) algorithm is preferred. This algorithm combines the Gauss-Newton method with the steepest descent method, and has the advantages of fast convergence speed and good stability, making it particularly suitable for solving fitting problems with a moderate number of parameters and high model nonlinearity.

[0071] When using a nonlinear regression algorithm (taking the LM algorithm as an example) to fit the sample Mueller matrix spectrum and the model-averaged Mueller matrix spectrum to obtain the optical critical dimensions, the specific steps are as follows: 1. Initialization: Set reasonable initial values ​​for the optical critical dimension parameters to be determined. (For example, based on process knowledge or rough estimates).

[0072] 2. Construct the objective function: Define the objective function. For the weighted sum of squared residuals: ; in, Let be the parameter vector to be determined. Number of wavelength points and These are the (i,j) elements of the measured and theoretical Mueller matrices, respectively. This represents the measurement uncertainty weight for the corresponding element.

[0073] 3. Iterative solution: a. Estimating using current parameters Using the numerical aperture distribution function established in this embodiment, the spectrum of the theoretical model is calculated. .

[0074] b. Calculate the objective function And its Jacobian matrix relative to each parameter.

[0075] c. According to the rules of the LM algorithm, solve the parameter increment equation and update the parameter estimates: .

[0076] d. Determine the convergence condition (e.g.) The change is less than the set threshold, or the parameter increment is sufficiently small. If convergence is not achieved, return to step a. Continue iterating from a new starting point; if convergence occurs, proceed to step 4.

[0077] 4. Output results: The parameter estimates at convergence. This serves as the final measurement result for the optical critical dimensions.

[0078] This embodiment calculates the aperture distribution by introducing a precise numerical aperture distribution function. This significantly improves the consistency between the theoretical model and the actual optical system state. This makes the objective function surface of nonlinear regression smoother and the global optimum closer to the true value, thereby greatly improving the accuracy, stability, and convergence speed of parameter fitting and effectively overcoming the problem of fitting divergence or getting trapped in local optima due to model mismatch.

[0079] The library matching algorithm is a non-iterative, fast fitting method. Its core lies in pre-calculating and storing a vast database (i.e., a "spectral library") covering all possible parameter combinations and their corresponding theoretical spectra using a theoretical model. During measurement, the experimental spectrum is compared with all theoretical spectra in the library, and the best match is found; the parameters corresponding to this match are taken as the measurement result.

[0080] The specific implementation process in this embodiment includes: 1. Spectral library construction (offline stage): a. Determine the possible range and step size of the key optical dimension parameters to be measured (such as film thickness).

[0081] b. For each combination of parameters in the parameter space, the corresponding model-averaged Mueller matrix spectrum is calculated using the numerical aperture distribution function (instead of a single angle) established in this invention.

[0082] c. Store all parameter combinations and their corresponding complete theoretical spectra (compressible storage) in a database to form a dedicated spectral library.

[0083] 2. Matching and Searching (Online Measurement Phase): a. Obtain the first sample Mueller matrix spectrum of the sample to be tested. .

[0084] b. With each theoretical spectrum in the spectral library Perform similarity calculations. Commonly used similarity criteria include root mean square error (RMSE) or correlation coefficient.

[0085] c. Choice and The theoretical spectrum with the highest similarity (e.g., the lowest RMSE).

[0086] d. The parameter combination corresponding to the theoretical spectrum can be directly output as the measurement result of optical critical dimensions or film thickness. Alternatively, sub-step accuracy results can be obtained through interpolation (such as secondary interpolation of the nearest few library spectra).

[0087] This embodiment integrates the numerical aperture distribution function into the spectral library construction process, ensuring that each theoretical spectrum in the library truly reflects the depolarization characteristics of the device. This fundamentally avoids the systematic errors introduced by using an ideal single-angle model for library construction. Although the library construction stage involves a large amount of computation, the single measurement speed is extremely fast, making it very suitable for online, high-speed, and large-scale detection scenarios. Its measurement accuracy directly depends on the density of the spectral library and the accuracy of the numerical aperture model provided by this invention.

[0088] This invention directly collects and analyzes the energy intensity distribution of real light spots, adaptively generates a discretized dot matrix and normalized weights, and establishes a numerical aperture distribution function that accurately matches the actual optical path state. This significantly improves the measurement accuracy and reliability of key optical dimensions or film thickness. Through weight calculation based on real light intensity and adaptive dot matrix distribution, the numerical aperture model closely matches the actual optical system. It possesses strong adaptability and can intelligently cope with various regular and irregular light spot shapes generated by different equipment optical paths. While ensuring accuracy, it optimizes the utilization of computational resources, achieving a balance between measurement efficiency and accuracy. This method requires no hardware modification and can be implemented only through algorithm upgrades. It is low-cost and easy to integrate into existing ellipsometric measurement equipment, and has extremely high application value in the fields of semiconductor manufacturing and precision optical measurement.

[0089] Figure 5 This is a functional module diagram of the ellipticity measurement correction device according to an embodiment of the present invention. Figure 5 As shown, the elliptic measurement correction device 20 includes: an acquisition module 21, a generation module 22, an establishment module 23, and a correction module 24.

[0090] Acquisition module 21 is used to acquire the energy intensity distribution of the light spot at the exit pupil surface of the incident arm lens; The generation module 22 is used to adaptively generate a discretized intensity distribution lattice based on the energy intensity distribution and calculate the normalized weight of each point; Module 23 is established to create a discretized numerical aperture distribution function based on the intensity distribution lattice, normalized weights, and lens numerical aperture parameters. The correction module 24 is used to correct the depolarization effect in spectral ellipsometric measurement using the numerical aperture distribution function, so as to obtain the measurement results of optical critical dimensions or film thickness.

[0091] Optionally, the generation module 22 performs the operation of adaptively generating a discretized intensity distribution dot matrix based on the energy intensity distribution and calculating the normalized weight of each point, specifically including: identifying the effective area of ​​the light spot using an adaptive threshold method according to the energy intensity distribution; matching the dot matrix configuration based on the shape parameters of the effective area and / or the light spot energy distribution; and calculating the normalized weight of each point based on the dot matrix configuration and the energy intensity distribution.

[0092] Optionally, the generation module 22 performs the operation of identifying the effective area of ​​the light spot using an adaptive threshold method, specifically including: selecting a pixel area with an energy intensity greater than the maximum intensity by a preset percentage as the effective area.

[0093] Optionally, the generation module 22 performs an operation based on the shape parameters of the effective area to match the dot matrix configuration, specifically including: calculating the rectangularity or roundness of the effective area; when the rectangularity is higher than a first threshold, determining that the light spot shape is rectangular, and matching a dot matrix configuration suitable for the rectangular light spot; when the roundness is higher than a second threshold, determining that the light spot shape is elliptical or circular, and matching a dot matrix configuration suitable for the elliptical or circular light spot.

[0094] Optionally, the generation module 22 performs an operation based on the shape parameters of the effective region to match the dot matrix configuration. Specifically, this includes: extracting the spatial distribution features of the light spot energy distribution in the effective region, and identifying whether there are step features formed by energy jumps in the energy distribution by calculating its energy gradient; if energy steps are identified, edge detection is performed on the light spot energy distribution, and the detected edges of each level of steps are used as spatial boundaries to divide the effective region into discrete regions that adapt to the dot matrix configuration; if no obvious energy steps are identified, multiple equal-energy-level envelopes are preset based on the peak ratio or curvature change rate of the energy distribution to virtually divide the effective region and obtain multiple regions that adapt to the dot matrix configuration.

[0095] Optionally, the generation module 22 performs the operation of calculating the normalized weights of each point, specifically including: mapping the matched dot matrix configuration to the effective area, treating each point as an integration unit; calculating the sum of the energy intensities of all pixels in each integration unit to obtain the integrated light intensity of each unit; summing all the integrated light intensities to obtain the total light intensity; and dividing the integrated light intensity of each unit by the total light intensity to obtain the normalized weights corresponding to that point.

[0096] Optionally, module 23 performs the operation of establishing a discretized numerical aperture distribution function, specifically including: calculating the incident angle and azimuth angle corresponding to each sampling point based on the normalized coordinates of each sampling point on the exit pupil plane and the lens numerical aperture parameters through geometric optical relationships, forming a set of triplet sequences composed of incident angle, azimuth angle and normalized weights, as the discretized numerical aperture distribution function.

[0097] Optionally, the correction module 24 performs the operation of correcting the depolarization effect in the spectral ellipsometric measurement using the numerical aperture distribution function to obtain the measurement results of the optical critical dimension or film thickness. Specifically, this includes: obtaining the ellipsometric spectrum of the test target sample to obtain the first sample Mueller matrix spectrum; calculating the first model average Mueller matrix spectrum based on the numerical aperture distribution function; and fitting the first sample Mueller matrix spectrum and the first model average Mueller matrix spectrum with a nonlinear regression algorithm or a library matching algorithm to obtain the optical critical dimension or film thickness.

[0098] Optionally, before performing the operation of correcting the depolarization effect in the spectral ellipsometric measurement using the numerical aperture distribution function, the correction module 24 is further configured to: perform ellipsometric measurement using a standard sample with known film thickness to obtain the Mueller matrix spectrum of the second sample; calculate the average Mueller matrix spectrum of the second model based on the numerical aperture distribution function; fit the Mueller matrix spectrum of the second sample and the average Mueller matrix spectrum of the second model using a nonlinear regression algorithm to obtain the fitted film thickness value; and fine-tune the lens numerical aperture parameters based on the fitted film thickness value to optimize the numerical aperture distribution function.

[0099] For further details regarding the implementation of the technical solutions for each module in the ellipticity measurement correction device of the above embodiments, please refer to the description in the ellipticity measurement correction method of the above embodiments, which will not be repeated here.

[0100] It should be noted that the various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For apparatus embodiments, since they are basically similar to method embodiments, the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments.

[0101] Please see Figure 6 , Figure 6 This is a schematic diagram of the structure of a computer device according to an embodiment of the present invention. Figure 6 As shown, the computer device 30 includes a processor 31 and a memory 32 coupled to the processor 31. The memory 32 stores program instructions. When the program instructions are executed by the processor 31, the processor 31 performs the steps of the elliptic measurement correction method described in any of the above embodiments.

[0102] The processor 31 can also be referred to as a Central Processing Unit (CPU). The processor 31 may be an integrated circuit chip with signal processing capabilities. The processor 31 can also be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. A general-purpose processor can be a microprocessor or any conventional processor.

[0103] See Figure 7 , Figure 7 This is a schematic diagram of the structure of the storage medium according to an embodiment of the present invention. The storage medium of this embodiment stores program instructions 41 capable of implementing the above-described correction method for ellipsometric measurement. These program instructions 41 can be stored in the storage medium in the form of a software product, including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks, or computer devices such as computers, servers, mobile phones, and tablets.

[0104] In the several embodiments provided in this application, it should be understood that the disclosed computer devices, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces, or indirect coupling or communication connection between devices or units, and may be electrical, mechanical, or other forms.

[0105] Furthermore, the functional units in the various embodiments of this invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated units described above can be implemented in hardware or as software functional units. The above are merely embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made based on the description and drawings of this application, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. A correction method for ellipticity measurement, characterized in that, include: The energy intensity distribution of the light spot is collected at the exit pupil surface of the incident arm lens; Based on the energy intensity distribution, a discretized intensity distribution lattice is adaptively generated, and the normalized weight of each point is calculated. Based on the intensity distribution lattice, the normalized weights, and the lens numerical aperture parameters, a discretized numerical aperture distribution function is established. The depolarization effect in spectral ellipsometric measurement is corrected using the numerical aperture distribution function to obtain the measurement results of optical critical dimensions or film thickness.

2. The correction method for ellipticity measurement according to claim 1, characterized in that, Based on the energy intensity distribution, a discretized intensity distribution lattice is adaptively generated, and the normalized weight of each point is calculated, including: Based on the energy intensity distribution, an adaptive thresholding method is used to identify the effective region of the light spot; Based on the shape parameters and / or spot energy distribution of the effective region, a matching dot matrix configuration is established; Based on the lattice configuration and the energy intensity distribution, the normalized weight of each point is calculated.

3. The correction method for ellipticity measurement according to claim 2, characterized in that, The step of identifying the effective region of the light spot using an adaptive threshold method includes: The effective region is a pixel region whose energy intensity is greater than a preset percentage of the maximum intensity.

4. The correction method for ellipticity measurement according to claim 2, characterized in that, Based on the shape parameters of the effective region, a matching dot matrix configuration is performed, including: Calculate the rectangularity or roundness of the effective region; When the rectangularity is higher than the first threshold, the shape of the light spot is determined to be rectangular, and a dot matrix configuration that is adapted to the rectangular light spot is matched. When the roundness is higher than the second threshold, the shape of the light spot is determined to be elliptical or circular, and a dot matrix configuration adapted to the elliptical or circular light spot is matched.

5. The correction method for ellipticity measurement according to claim 2, characterized in that, Based on the light spot energy distribution in the effective region, a matching dot matrix configuration is established, including: Spatial distribution features of the light spot energy distribution in the effective area are extracted, and the energy gradient is calculated to identify whether there are step features formed by energy jumps in the energy distribution; If an energy step is detected, edge detection is performed on the energy distribution of the light spot. The detected edges of each step are used as spatial boundaries, and the effective area is divided into discrete areas with an adaptive dot matrix configuration. If no obvious energy step is identified, multiple equal-energy-level envelopes are preset based on the peak ratio or curvature change rate of the energy distribution to virtually divide the effective region and obtain multiple regions adapted to the lattice configuration.

6. The correction method for ellipticity measurement according to claim 2, characterized in that, The calculation of the normalized weights for each point includes: The matched dot matrix configuration is mapped to the effective region, and each dot is treated as an integration unit; The sum of the energy intensities of all pixels within each integration unit is calculated to obtain the integrated light intensity of each unit; Summing up all the integrated light intensities yields the total light intensity. Divide the integrated light intensity of each unit by the total light intensity to obtain the normalized weight corresponding to that point.

7. The correction method for ellipticity measurement according to claim 1, characterized in that, The establishment of the discretized numerical aperture distribution function includes: Based on the normalized coordinates of each sampling point on the exit pupil plane and the lens numerical aperture parameters, the incident angle and azimuth angle corresponding to each sampling point are calculated through geometric optics relationships, forming a set of triplets consisting of the incident angle, the azimuth angle and the normalized weights, which serve as the discretized numerical aperture distribution function.

8. The correction method for ellipticity measurement according to claim 1, characterized in that, The method of using the numerical aperture distribution function to correct the depolarization effect in spectral ellipsometric measurement to obtain the measurement results of optical critical dimensions or film thickness includes: The ellipsometry of the target sample was obtained by testing, and the Mueller matrix spectrum of the first sample was obtained. Calculate the first model's average Mueller matrix spectrum based on the numerical aperture distribution function; By fitting the Mueller matrix spectrum of the first sample with the average Mueller matrix spectrum of the first model, the optical critical dimension or film thickness is obtained.

9. The correction method for ellipticity measurement according to claim 1, characterized in that, Before correcting the depolarization effect in spectral ellipsometric measurements using the numerical aperture distribution function, the method further includes: Ellipsometry was performed using a standard sample with a known film thickness to obtain the Mueller matrix spectrum of the second sample; The second model average Mueller matrix spectrum is calculated based on the numerical aperture distribution function; The Mueller matrix spectrum of the second sample is fitted with the average Mueller matrix spectrum of the second model to obtain the fitted film thickness value; The lens numerical aperture parameter is finely adjusted based on the fitted film thickness value to optimize the numerical aperture distribution function.

10. The correction method for ellipticity measurement according to claim 8 or 9, characterized in that, The Mueller matrix spectrum of the first sample is fitted to the average Mueller matrix spectrum of the first model using a nonlinear regression algorithm or a library matching algorithm, and / or the Mueller matrix spectrum of the second sample is fitted to the average Mueller matrix spectrum of the second model using a nonlinear regression algorithm or a library matching algorithm.

11. A correction device for ellipticity measurement, characterized in that, include: The acquisition module is used to acquire the energy intensity distribution of the light spot at the exit pupil surface of the incident arm lens; The generation module is used to adaptively generate a discretized intensity distribution lattice based on the energy intensity distribution, and calculate the normalized weight of each point; A module is established to establish a discretized numerical aperture distribution function based on the intensity distribution lattice, the normalized weights, and the lens numerical aperture parameters. The correction module is used to correct the depolarization effect in spectral ellipsometric measurement using the numerical aperture distribution function, so as to obtain the measurement results of optical critical dimensions or film thickness.

12. A computer device, characterized in that, The computer device includes a processor and a memory coupled to the processor, the memory storing program instructions that, when executed by the processor, cause the processor to perform the steps of the correction method for ellipsometric measurement as described in any one of claims 1-10.

13. A storage medium, characterized in that, The system stores program instructions capable of implementing the correction method for ellipsometric measurement as described in any one of claims 1-10.

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